Figure 15. Topological control of conduction states in artificially created 180° domain walls due to head–head and tail–tail driven charge segregation as imaged via (a) vertical amplitude and (b) vertical phase images of a ring written in BiFeO3 by application of  +9 V within a single lateral domain. Polarization vectors are shown in the phase image. (c) c-AFM image of the written ring domain taken using tip bias of  −2.8 V. (d) Spectrogram of the current as a function of angle and distance from the outer ring of the ferroelectric domains wall (Reprinted with permission from [554]. Copyright 2012 American Chemical Society). (e) Nanobeam electron diffraction strain mapping image of the out-of-plane strain (relative to the substrate GdScO3) in compositionally-graded PbZr1−xTixO3 heterostructures. The image shows that large out-of-plane strain gradients stabilize needle-like ferroelastic domain structures. High-field (~1/2 Ec) out-of-plane band excitation PFM amplitude images of (f) homogeneous PbZr0.2Ti0.8O3 and (g) compositionally-graded heterostructures. These images reveal that the needle-like ferroelastic domains are highly labile in the out-of-plane direction, giving rise to locally enhanced piezoresponse (Reprinted with permission from [558]. Copyright 2016 Nature Publishing Group).

Figure 14. (a) Magnetoelectric hysteresis curve at 100 K showing the magnetic response of a PbZr0.2Ti0.8O3/La0.2Sr0.8MnO3 heterostructure as a function of applied electric field. The two magnetization values correspond to the modulation of the magnetization of the La0.2Sr0.8MnO3 layer. The inset represents the magnetic and electric states of the La0.2Sr0.8MnO3 and PbZr0.2Ti0.8O3 layers, respectively. The size of the arrows indicates, qualitatively, the magnetization amplitude (Reprinted with permission from [509]. Copyright 2009 John Wiley and Sons). (b) Schematic model of the spin configurations in La0.2Sr0.8MnO3 at the PbZr0.2Ti0.8O3 interface for the depletion and accumulation states, showing the changes in the Mn and O orbital states and the expected changes in the magnetic moment per layer. The arrows indicate the spin orientation in the Mn cations and n denotes number of unit cells below the PbZr0.2Ti0.8O3 layer. The Mn d orbitals are drawn in orange and grey, and the lobes of the p orbitals are shown around the oxygen atoms (red) (Reprinted figure with permission from [510]. Copyright 2010 by the American Physical Society). (c) Variation of the magnetization in FeRh/BaTiO3 heterostructure with the applied voltage at 385 K, after heating under an external voltage of  +21 V. The symmetric dependence of magnetization indicates that the voltage-induced strain effect from the ferroelectric BaTiO3 dominates the magnetoeletric response. The inset shows the voltage dependence of the out-of-plane parameter of FeRh at 390 K (Reprinted with permission from [514]. Copyright 2014 Nature Publishing Group). (d) Ferroelectric (FE) and ferromagnetic (FM) microstructure after CoFe film growth on BaTiO3 and (e) after the application of an out-of-plane electric field of 10 kV cm−1; imaged using optical polarization microscopy. The polarization direction and lattice elongation of the BaTiO3 substrate is indicated by black rectangles with arrows, whereas the orientation of the strain-induced magnetic easy axis is indicated by the white rectangles with double-headed arrows, and the magnetization direction in zero applied magnetic field is indicated by the white arrows. Exact correlation between the ferroic domains patterns can be seen due to the strain transfer at the heterostructure interface (Reprinted with permission from [516]. Copyright 2012 Nature Publishing Group).

Figure 13. (a) Schematic illustration indicating the fundamental principles of flexoelectricity. (b) Illustration of methodologies for generating strain gradients through controlled defects. The top shows a diagram indicating strain relaxation caused by oxygen vacancies in HoMnO3; the bottom, indicates how growth pressure can be used to tune the magnitude of strain relaxation and, in turn, the flexoelectric effects (reproduced from Reprinted with permission from [405]. Copyright 2012 American Chemical Society. Reprinted with permission from [406]. Copyright 2011 by the American Physical Society). (c) Phase diagram and lattice parameter evolution within the PbZr1−xTixO3 system which indicates how compositionally-graded heterostructures with large strain gradients can be formed (Reprinted with permission from [415]. Copyright 2015 American Chemical Society). (d) Polariation-electric field hysteresis loops of various single-composition and compositionally-graded heterostructures demonstrating the influence of flexoelectric effects in generating large built in potentials (Adapted from [403]. Copyright 2013 American Chemical Society). (e) Plot of measured built-in potential as a function of film thickness for compositionally-graded heterostructures of various thickness and compositional-gradient form. The dashed line and small diamond markers represents an estimation of the built-in potentials based on the flexo-chemo-electric coefficient of the 50 nm (20,80) heterostructures. This work indicates that the built-in potentials are significantly enhanced by the presence of large local strain gradients such as those arising from ferroelastic domains walls and/or transitions through the MPB (Reprinted with permission from [415]. Copyright 2015 American Chemical Society). (f) Low-field dielectric permittivity measured as a function of frequency for various single-layer and compositionally-graded heterostructures highlighting the role of the built-in potential in significantly suppressing the intrinsic and extrinsic contributions to the dielectric permittivity (Reprinted with permission from [404]. Copyright 2013 John Wiley & Sons).

Figure 12. (a) and (b) Crystallographic structure of Ca3−xSrxTi2O7 with the orthorhombic A21am space group. The red (blue), white (dark green), and light-blue spheres represent Ca/Sr in the rock-salt (R) block and perovskite (P) block, planar (apical) oxygen of the TiO6 octahedra, and Ti at the center of the TiO6 octahedra, respectively. The red and blue arrows depict Ca/Sr displacement along [100] ║ a in the R and the P block, respectively. (c) Polarization-electric field hysteresis loops for Ca3−xSrxTi2O7 (x  =  0, 0.54, 0.85) single crystals at room temperature with electric fields applied along the [110] (along the twin boundaries) at frequency f  =  260 Hz. (Reprinted with permission from [395]. Copyright 2015 Nature Publishing Group).

Figure 11. (a) Polarization-electric field hyseteresis loops for Sm-doped BiFeO3 films showing a clear transition from ferroelectric to antiferroelectric behavior with increasing Sm-content. Such behavior is not observed in (b) La-doped BiFeO3 due to the smaller ionic radius of the dopant ions (Reprinted with permission from [367]. Copyright 2011 AIP Publishing LLC). Both (c) ε33 and (d) d33 improve as a function of rare-earth dopant-concentration to the respective MPB compositions (Reprinted with permission from [369]. Copyright 2010 AIP Publishing LLC). (e) Bright-field STEM image of a Srn+1TinO3n+1 thin film with n  =  6 showing alternating perovskite (dark) and SrO2 (light) layers. (f) In-plane dielectric tunability of the same Srn+1TinO3n+1 thin films with n  =  6 at microwave frequencies and (inset) frequency-dependent dielectric response at various applied bias fields (Reprinted with permission from [370]. Copyright 2013 Nature Publishing Group). Reciprocal space maps about the 103-diffraction condition of BaTiO3 films grown at laser fluence of (g) 1.5 and (h) 2.7 J cm−2 that reveal that lattice expansion can be tuned using the growth process by  >4%. (i) Ferroelectric hysteresis loops of BaTiO3 films measured at 10 kHz which show ferroelectric behavior up to 500 °C and (inset) revealing the temperature dependent evolution of the polarization and dielectric constant from 25 to 500 °C (Adapted with permission from [380]. Copyright 2014 John Wiley and Sons).

Figure 10. Lateral and vertical (Acosθ, combining phase θ and amplitude A, inset) PFM images for equilibrium domain structures of (a) (001)-, (b) (101)-, and (c) (111)-oriented PbZr0.2Ti0.8O3/La0.7Sr0.3MnO3/SrTiO3 heterostructures. (d) The dielectric permittivity measured at an ac excitation voltage of 50 mV for (001)-, (101)-, and (111)-oriented PbZr0.2Ti0.8O3 thin films (solid line). The dashed lines show the predicted permittivity (including intrinsic and extrinsic contributions) from GLD models. (e) Polarization - electric field hysteresis loops measured at 1 kHz for (001)-, (101)-, and (111)-oriented PbZr0.2Ti0.8O3 thin films (Reprinted from [353, 354]. Copyright 2014 Nature Publishing Group).

Figure 9. Strain-driven multiferroism in EuTiO3 epitaxial thin films. (a) Predicted effect of epitaxial strain on EuTiO3. (b) Temperature-dependence of the magnetization measured using both MOKE and SQUID magnetometry. (c) SHG hysteresis loop (blue) and corresponding polarization loop (red) for EuTiO3 on DyScO3 (110) at 5 K. The data reveals that epitaxial EuTiO3 thin films on DyScO3 are ferroelectric and ferromagnetic below 5 K. (Reprinted with permission from [328]. Copyright 2010 Nature Publishing Group).

Figure 8. In short-period PbTiO3/SrTiO3 superlattices, the ferroelectric mode (a) FEz, couples to two antiferrodistortive modes (b) AFDzi and (c) AFDzo, inducing an improper ferroelectric state. The particular set of structural distortions that condenses is sensitive to biaxial strain and thus other ground states with different couplings can be engineered (Reprinted with permission from [306]. Copyright 2008 Nature Publishing Group). (d) Observation of vortex/anti-vortex structures in intermediate periodicity (PbTiO3)10 / (SrTiO3)10 superlattices using cross-sectional, atomic-scale imaging using STEM (the overlaid polarization vector maps represent the locally extracted polar distortion). (e) A magnified image of a single vortex/anti-vortex pair where the polarization state within such pairs can be visualized. (f) Phase-field simulations of the same superlattice structure also predicting the vortex/anti-vortex pairs. (g) The curl of polarization (∇   ×  P) for a single vortex pair, extracted from the cross-section STEM polarization vector map (Reprinted with permission from [324]. Copyright 2016 Nature Publishing Group).

Figure 7. (a) AFM image (left) and vertical PFM image (right) of a 100 nm BiFeO3/La0.5Sr0.5CoO3/LaAlO3 (001) film in the as-grown state (0 V) and after being poled in the box at various voltages (all images are 1  ×  1 μm). At the center is a schematic hysteresis loop that shows the pathway to enhanced electromechanical responses (Adapted from [262]. Copyright 2011 John Wiley and Sons). (b) Piezoelectric hysteresis loops from T-like (blue curve), R-like (green curve) and mixed-phase (purple and orange curves) BiFeO3 thin films, grown by pulsed-laser deposition (PLD) and chemical vapor deposition (CVD), measured in capacitors with a diameter of 32 μm (Reprinted with permission from [286]. Copyright 2011 Nature Publishing Group). (c) XMCD-PEEM image of a mixed phase BiFeO3 film (Reprinted with permission from [287]. Copyright 2011 Nature Publishing Group).

Figure 6. Evolution of the (a) energy and (b) c/a lattice parameter ratio of BiFeO3 as a function of in-plane strain. This data shows the presence of two phases—both with monoclinic symmetry—the highly-distorted T-like phase (left) and an R-like phase derived from the parent phase. The lattice mismatch between a number of commonly used and tested oxide substrates are shown as dashed lines (Reprinted with permission from [249]. Copyright 2009 AAAS Publishing). (c) High-resolution AFM image of a mixed-phase region, and (d) high-resolution TEM image of the boundaries between R- and T-like regions (Reprinted with permission from [249]. Copyright 2009 AAAS Publishing). A smooth transition between phases is observed; no dislocations or defects are found at the interface. (e) AFM topography and (f) line-trace along the dashed line of a 140 nm thick BiFeO3 / LaAlO3 (001) thin film. (g) RSM about the 002-diffraction condition of LaAlO3 for a 130 nm-thick BiFeO3/LaAlO3 (001) thin film (Adapted from [262]. Copyright 2011 John Wiley and Sons).

Figure 5. (a) Schematic illustration, (b) surface topography, (c) vertical phase, and (d) lateral amplitude images of 71°-striped BiFeO3 possessing a flat surface topography and (e) schematic illustration, (f) surface topography, (g) vertical phase, and (h) lateral amplitude images of 109°-domain variants BiFeO3 showing a puckered surface structure. (i) Lateral PFM phase image of BiFeO3 with 180° domain structure; the inset shows a schematic illustration of the domain structure where the arrows represent the directions of the spontaneous polarization. (j) Cross-sectional, dark-field TEM image (top) and RSMs (bottom) about the 020O-(110-) diffraction conditions of GdScO3 (pseuodocubic BiFeO3) with the x-ray beam incident along the [001]O, of a 14 nm thick BiFeO3 / GdScO3 (010)O heterostructure with a 180° domain structure. Arrows indicate the positions of satellite peaks due to the periodic domain structure. (k) Room-temperature, in-plane magnetic hysteresis loops for a Pt/Co0.9Fe0.1/BiFeO3/GdScO3 (010)O heterostructure with a 180° domain structure (measured along in-plane [001]O). A loop of similarly grown Pt/Co0.9Fe0.1/GdScO3 (010)O heterostructure is shown for comparison. (Figures (i)-(l) are adapted with permission from [241]. Copyright 2015 American Chemical Society).

Figure 4. (a) Phase diagram of BaTiO3 films as a function of temperature and misfit strain, with TP (tetragonal paraelectric), TF (tetragonal ferroelectric), OF (orthorhombic ferroelectric), and MF (monoclinic ferroelectric) phases noted, and (b)–(e) representative domain morphologies in BaTiO3 films at different temperatures and misfit strains (Reprinted with permission from [203]. Copyright 2006 AIP Publishing LLC). (f) Strain-composition phase diagram for PbZr1−xTixO3 thin films showing the pyroelectric coefficient at 300 K for the various equilibrium polydomain states (adapted from [212]). (g) The measured pyroelectric coefficient (squares) as a function of percentage of a domains in polydomain PbZr0.2Ti0.8O3 thin films. The orange line represents the intrinsic response and the green line represents the primary response (intrinsic  +  extrinsic) calculated using polydomain GLD theory. The blue line indicates the trend expected assuming an average thermal expansion coefficient of 10.9  ×  106 K−1 (Adapted from [213]. Copyright 2012 by the American Physical Society). PFM amplitude and phase (inset) images showing the sequence of 180° switching from (h) the initial 'parallel' c/a domain structure with homogeneous phase to (i) monodomain c domain with further switching leading to the creation of (j) ferroelastic a domains oriented both vertically and horizontally (Reprinted with permission from [214]. Copyright 2014 AIP Publishing LLC). (k) Lateral PFM phase images (scale bar range, 0–70°) of areas of 2  ×  2 μm2 of an in-plane polarized 30 nm-thick PbxSr1−xTiO3 film. Four types of areas are observed (marked by the black squares), defining coarse-scale 'superdomains'. The polarization orientation in the nanodomains is represented by arrows for the four types of domain variants (Reprinted with permission from [220]. Copyright 2014 Nature Publishing Group).

Figure 3. (a) Diagram showing the various nomenclatures used to describe ferroelectric phases based on their polarization direction. Tetragonal (T): T(c) P1  =  P2  =  0, P3  ≠  0; T(a1) P2  =  P3  =  0, P1  ≠  0; T(a2) P1  =  P3  =  0, P2  ≠  0. Monoclinic (M): MC(ca) P1  ≠  0, P2  =  0, P3  ≠  0; MA(r) P1  =  P2  ≠  0  <  P3  ≠  0; MB(r) P1  =  P2  ≠  0  >  P3  ≠  0; MC(ca*) P1  =  0, P2  ≠  0, P3  ≠  0; MC(aa*) P1  ≠  0, P2  ≠  0, P3  =  0. Orthorhombic (aa): O P1  =  P2  ≠  0, P3  =  0. Rhombohedral (R): R P1  =  P2  =  P3  ≠  0. (b) Phase-field predictions for the misfit-strain-temperature phase diagram for (001)-oriented SrTiO3 assuming a monodomain state for all structural and ferroelectric phases (Reprinted with permission from [20]. Copyright 2008 John Wiley and Sons. Adapted with permission from [111]). The letters T, O, R, and M used in the phase notations indicate tetragonal, orthorhombic, rhombohedral, and monoclinic crystallographic symmetries, respectively. The superscript 'P,' 'S,' or 'F' indicates whether the phase is paraelectric, antiferrodistortive, or ferroelectric, respectively. (c) Temperature-dependent in-plane dielectric constant (εr) at a measurement frequency ( f ) of 10 GHz for 50 nm thick films of SrTiO3 on DyScO3 (110) and (LaAlO3)0.29(Sr0.5Al0.5TaO3)0.71 (001) substrates corresponding to epitaxial strains of  +0.9% and –0.9%, respectively (Reprinted with permission from [112]. Copyright 2004 Nature Publishing Group). (d) and (e) BaTiO3 temperature-stress diagram comparing ab initio predictions (Reprinted with permission from [126]. Copyright 2004 by the American Physical Society) with those from phenomenological thermodynamic calculations (Reprinted from [33] by permission of Taylor & Francis Ltd, www.tandfonline.com). (f) In-plane diffuse x-ray scattering profiles about the PbTiO3 303-diffraction condition for various thicknesses and temperatures. In each case the region shown extends  ±0.2 reciprocal lattice units in the in-plane reciprocal space coordinates H and K. The broadening of the central Bragg peak in the H direction is due to instrumental resolution limits. Inset shows orientation of stripe domains (Reprinted with permission from [153]. Copyright 2004 AAAS Publishing).

Figure 2. Survey of lattice parameters of commercially available substrate materials (bottom section), a select list of perovskite electrode materials (middle section), and ferroelectric, incipient ferroelectric, and anti-ferroelectric materials (top section).

Figure 5. a,b, Voltage-lapse images near an a domain in homogeneous PbZr0.2Ti0.8O3 (a) and compositionally graded PbZr1−xTixO3 (b) heterostructures as imaged throughout a switching cycle. c,d, Negative coercive field (Ec−), positive coercive field (Ec+) and voltage offset for the same homogeneous PbZr0.2Ti0.8O3 (c) and compositionally graded PbZr1−xTixO3 (d) heterostructures extracted from fits of piezoelectric hysteresis loops. Colour scales based on an identical fraction of the average fitted coercive field. e,f, High-field, local piezoresponse of the same homogeneous PbZr0.2Ti0.8O3 (e) and compositionally graded PbZr1−xTixO3 (f) heterostructures revealing inverted responses between the two heterostructure variants. All scale bars are 500 nm.

Figure 4. a, Typical, macroscopic ferroelectric hysteresis loop of a compositionally graded PbZr1−xTixO3 heterostructure measured at 10 kHz. b–f, Corresponding band-excitation switching spectroscopy amplitude and phase images of the same compositionally graded PbZr1−xTixO3 heterostructure measured at various stages (as labelled) of ferroelectric switching. All scale bars are 250 nm. g–j, Schematic illustrations of the switching process in the compositionally graded PbZr1−xTixO3 heterostructures. The colour key on the bottom right labels the polarization directions in the illustrations.

Figure 3. a, Typical, macroscopic ferroelectric hysteresis loop of a homogeneous PbZr0.2Ti0.8O3 heterostructure measured at 10 kHz. b–f, Corresponding band-excitation switching spectroscopy amplitude and phase images of the same homogeneous PbZr0.2Ti0.8O3 heterostructure measured at various stages (as labelled) of ferroelectric switching. All scale bars are 500 nm. g–j, Schematic illustrations of the switching process in the homogeneous PbZr0.2Ti0.8O3 heterostructures. Only the positive-bias half of the switching process is shown. Switching from the down-poled to the up-poled state happens in a similar manner, but with polarization of opposite sense. The colour key on the bottom right labels the polarization directions in the illustrations.

Figure 2. a, High-angle, angular dark-field scanning transmission electron microscopy image of a compositionally graded heterostructure revealing the presence of ferroelastic domains with needle-like shapes. b–d, Nanobeam diffraction-based strain mapping of compositionally graded heterostructures reveals the out-of-plane (b) and in-plane (c) strain state of the film as well as the local unit-cell rotation (d). All scale bars are 25 nm. e, Thickness-dependent, average in-plane and out-of-plane strain calculated from the nanobeam diffraction strain mapping. All strain is normalized to the substrate.

(a) In thin, unrelaxed films, step-flow growth persists; the arrows indicate the possibility of attachment of adatoms either directly to the step edges or after being reflected by the descending edge due to the ES barrier (inset shows the adatom potential energy landscape). (b) As the thickness increases, there is an onset of a kinetic instability due to dislocation formation and nucleation of islands in the capture zones (inset shows the adatom potential energy landscape is lowered, red color, due to the dislocation strain field). (c) With further increased film thickness, formation of an ordered array of dislocations induces ordered, multi-terrace island formation. (d) Continued film growth, leads to formation of multi-terrace islands and island coarsening.

Figure 5. Atomic force microscopy images and illustration of island identification procedure for heterostructures with thicknesses of (a) 55 nm, (b) 65 nm, (c) 90 nm, and (d) 150 nm. (e) Measured island density as a function of increasing film thickness.

Figure 4. (a) Calculated variation of compressive in-plane strain at the film surface as a function of film thickness. The data, from top to bottom, represent the case for pseudomorphically-strained (blue), 40 nm thick (purple), 100 nm thick (magenta), and fully-relaxed (red) heterostructures and show periodic strain modulations on the surface of 40 nm and 100 nm thick films due to the buried misfit dislocation array (T-symbol). (b) Schematic illustration of the variation in the adatom binding energy on the surface-red and blue areas are regions with stronger and weaker binding energy, respectively. (c) Schematic illustration of the in-plane lattice parameters on the surface of a film under a partially relaxed biaxial strain-red and blue areas are under less and more compressive strain, respectively. (d) The measured topography of a 55 nm thick PbZr0.2Ti0.8O3 heterostructure showing aligned wedding-cake structures. (e) Cross-section, dark-field TEM image of the same heterostructure taken under the g = (200) two beam condition along the [012] zone axis showing the presence of dislocations (white arrows point to dislocations located at the PbZr0.2Ti0.8O3/SrRuO3 interface) and corresponding strain fields. (f) Zoom-in image of the strain-induced contrast from the dislocation strain fields.

Figure 3.In-plane strain relaxation (%, red circles) and surface ripple density (μm−1, blue squares) as a function of film thickness.

Figure 2. (a) θ–2θ X-ray diffraction patterns for various thin film heterostructures reveal single-phase and epitaxial films. Asymmetric reciprocal space mapping studies about the 103-diffraction conditions of heterostructures with PbZr0.2Ti0.8O3 thicknesses of (b) 25 nm, (c) 55 nm, and (d) 150 nm. Diamond symbols (black, open) represent the bulk, fully-relaxed film peak position.

Figure 4. Pyroelectric coefficients as functions of temperature and volume fraction along (a) [100], (b) [010], and (c) [001] of the NdScO3/BaTiO3/NdScO3 trilayer heterostructures.

Figure 3. Temperature–volume fraction (a) ferroelectric phase diagram and (b) total equilibrium polarization of a NdScO3/BaTiO3/NdScO3 trilayer heterostructure. Equilibrium polarization as a function of temperature for NdScO3/BaTiO3/NdScO3 trilayer heterostructures of (c) ϕF ≈ 0 and 1 and (d) ϕF = 0.4, 0.5, and 0.7 with the origin of the vertical axis coordinate at 0, 0.1, and 0.2 C/m2, respectively.

Figure 2. (a) Volume fraction–misfit strain phase diagram of non-ferroelectric/BaTiO3/non-ferroelectric free-standing trilayer heterostructure at T = 25 °C assuming equivalent elastic compliances between the layers (SijF = SijNF). Elastic compliance–misfit strain phase diagram of non-ferroelectric/BaTiO3/non-ferroelectric free-standing trilayer heterostructure for (b) S11NF − S12NF = 12.25 × 10−12 m2/N and (c) S11NF − S12NF = 5.38 × 10−12 m2/N with equal layer thickness (ϕF = 0.5) at T = 25 °C.

Figure 5. Room temperature dielectric permittivity (measured at Vac = 8 mV, error <7%) as a function of frequency for PbZryTi1–yO3 ↔ PbZrxTi1–xO3/SrRuO3/GdScO3 compositionally-graded heterostructures (sample name: (x,y)) for various (a) (20,80) heterostructure thicknesses and (b) various 100 nm thick compositional-gradient designs.

Figure 4. Room temperature polarization–electric field hysteresis loops of PbZryTi1–yO3 ↔ PbZrxTi1–xO3/SrRuO3/GdScO3 heterostructures (sample name: (x,y)) measured at 1 kHz of various (a) (20,80) heterostructure thicknesses and (b) various 100 nm thick compositional-gradient designs. (c) Plot of measured built-in potential as a function of film thickness for all compositionally-graded heterostructures studied. Dashed line and small diamond markers represents an estimation of the built-in potentials based on the flexo-chemo-electric coefficient of the 50 nm (20,80) heterostructures.

Figure 3. Vertical phase piezoresponse force microscopy images of PbZr0.8Ti0.2O3 ↔ PbZr0.2Ti0.8O3/SrRuO3/GdScO3 (110) heterostructures (sample name: (x,y)) (a) 50 nm (20,80), (b) 100 nm (20,80), (c) 150 nm (20,80), (d) 100 nm (20,45), and (e) 100 nm (40,60). A vertical amplitude piezoeresponse force microscopy image is provided as an inset in each of the figures.

Figure 2. Reciprocal space mapping about the 103-diffraction conditions for PbZryTi1–yO3 ↔ PbZrxTi1–xO3/SrRuO3/GdScO3 (110) heterostructures (sample name: (x,y)) (a) 50 nm (20,80), (b) 75 nm (20,80), (c) 100 nm (20,80), (d) 150 nm (20,80), (e) 100 nm (20,45), and (f) 100 nm (40,60). Dashed lines represent the coherently strain (vertical) and cubic (angled) lattice parameters and the expected peak positions for bulk (black) and strained (orange) versions of the parent phases are labeled in each graph. The percentage of strain relaxation is also noted.

Figure 6. a) Typical dielectric permittivity as a function of frequency measured at increasing background fields for a 75 nm PbZr0.52Ti0.48O3/25 nm SrRuO3/SrTiO3 (001) heterostructure. Extracted zero frequency permittivity as a function of increasing background fields for b) PbZr0.2Ti0.8O3, c) PbZr0.8Ti0.2O3, and PbZr0.52Ti0.48O3 heterostructures grown on (d) SrTiO3 (001), e) DyScO3 (110), and f) GdScO3 (110) substrates. Regions where linear fits were computed are represented by the purple, red, and green dashed lines for the intrinsic, intermediate, and extrinsic regimes, respectively.

Figure 5. a) Dielectric permittivity and b) loss tangent for all heterostructure variants displayed as a function of ac excitation bias represented as field. Frequency dependence of the c) dielectric permittivity and d) loss tangent for all heterostructure variants. e) Fits to the Rayleigh regime (marked by the black dashed lines and red linear fits in a) reveal values of for εinit and α.

Figure 4. Band excitation piezoresponse force microscopy amplitude images following single point band excitation piezoresponse force switching studies for 75 nm PbZr0.52Ti0.48O3/25 nm SrRuO3 heterostructures grown on a) SrTiO3 (001) and b) NdScO3 (110) substrates. c) The average switched area extracted from the band excitation piezoresponse force phase image is represented in a histogram – indicating on average larger switched domains in heterostructurs on SrTiO3 as compared to the heterostructures on DyScO3 and NdScO3 substrates.

Figure 3. Electrical measurement of 75 nm PbZr0.52Ti0.48O3/25 nm SrRuO3 on various substrates. a) Current-voltage measurements (including, for comparison, 100 nm PbZr0.2Ti0.8O3/25 nm SrRuO3/GdScO3 (110) heterostructure). b) Ferroelectric hysteresis loops measured at 1 kHz. c) Ferroelectric hysteresis loops for a PbZr0.52Ti0.48O3/SrRuO3/SrTiO3 (001) heterostructure taken at various frequencies. The inset shows the transition region observed in ferroelectric hysteresis loops at 30 mHz, indicated by the black arrow. All hysteresis loops are composed of a minimum of 150 data points.

Figure 2. a) θ-2θ X-ray diffraction pattern about the 002-diffraction condition for 75 nm PbZr0.52Ti0.48O3/25 nm SrRuO3 heterostructures grown on SrTiO3 (001), DyScO3 (110), and NdScO3 (110) substrates (bottom-to-top of graph). Asymmetric reciprocal-space mapping studies about the 103- and 332-diffraction condition for heterostructures grown on b) SrTiO3 (001), c) DyScO3 (110), and d) NdScO3 (110) substrates. Substrate and film peak location marked by the circular marker. The bulk (solid) and strained (open) PbZr0.52Ti0.48O3 tetragonal peak is indicated with a diamond

Figure 5. Room-temperature dielectric permittivity–voltage butterfly loops of compositionally (a) up-graded and (b) down-graded variants.

Figure 4. Room temperature, 1 kHz polarization-electric field hysteresis loops for: a) down-bilayer and -graded variants, and b) up-bilayer and -graded variants. c) Dielectric permittivity and d) loss tangent for each of the six sample variants as a function of frequency.

Figure 3. Piezoresponse force microscopy images of: a) single-layer PbZr0.2Ti0.8O3 (vertical phase), b) single-layer PbZr0.8Ti0.2O3 (vertical phase), c) up-bilayer (vertical phase), d) down-bilayer (lateral amplitude), e) up-graded (vertical phase), and f) down-graded (lateral amplitude) variants.

Figure 2. Time-of-flight secondary-ion mass spectra for single-layer (a) PbZr0.2Ti0.8O3 and (b) PbZr0.8Ti0.2O3 and compositionally (c) up-graded and (d) down-graded variants. Reciprocal-space mapping about the 103 and 332-diffraction conditions for: (e) single-layer PbZr0.2Ti0.8O3, (f) single-layer PbZr0.8Ti0.2O3, (g) up-bilayer, (h) down-bilayer, (i) up-graded, and (j) down-graded variants. Expected peak positions for bulk (black) and strained (orange) versions of the parent phases are labeled in each graph. Note that when appropriate and distinct, we distinguish between peaks arising from Zr-rich and Ti-rich PbZr1-xTixO3 as PZTR and PZTT, respectively.

Figure 4. Evolution of (a) in-plane (P1 = P2) and (b) out-of-plane (P3) polarization across the thickness of a 100 nm thick compositionally down-graded film at 300 K. For comparison, the same polarization components are calculated for coherently strained films (black dashed line labeled no relaxation). Again results from all four variations of the strain relaxation model are provided including Y =G, Tg =300 K (red), Y >G, Tg = 300 K (green), Y =G, Tg =800K(blue), andY >G, Tg =800K(orange).

Figure 3. Evolution of (a) in-plane (P1 = P2) and (b) out-of-plane (P3) polarization across the thickness of a 100 nm thick compositionally up-graded film at 300 K. For comparison, the same polarization components are calculated for coherently strained films (black dashed line labeled no relaxation). Again results from all four variations of the strain relaxation model are provided including Y=G, Tg =300 K (red), Y>G, Tg =300K (green), Y=G, Tg =800K (blue), and Y >G, Tg =800 K (orange).

Figure 2. Evolution of strain in compositionally graded thin films including the theoretical lattice misfit strain (um) at 300 K (black dashed line) and 800 K (grey dash-dot line) as well as the total strain (u) at 300 K (as calculated by the various model variants) for compositionally (a) up-graded and (b) down-graded thin films. The magnitude of the strain relieved by dislocation formation (|u − um|) is also shown for compositionally (c) up-graded and (d) down-graded films. The four model variants considered are Y = G, Tg =300 K(red),Y >G, Tg = 300K (green), Y =G, Tg = 800K (blue), and Y > G, Tg = 800 K (orange) and the striped grey regions represent the values bounded by the various models.

Figure 4. The measured pyroelectric coefficient (filled red squares) as a function of percentage a-domains in polydomain PbZr0.2Ti0.8O3 thin films. The dashed orange line is the intrinsic response and the dashed blue line is the primary response (intrinsic + extrinsic) calculated using polydomain GLD theory. The open green squares indicate the sum of primary + secondary contributions to the pyroelectric coefficient for each film-substrate combination and the dashed green line indicates the trend expected assuming an average thermal expansion coefficient of 10.9  x 106 K-1 for all the substrates.

Figure 3. (a) Schematic of the phase-sensitive measurement technique utilizing a sinusoidal temperature oscillation. (b) Typical trace of the applied temperature variation and (c) the measured sinusoidal pyroelectric current on a 100 µm diameter PbZr0.2Ti0.8O3 capacitor.

Figure 2. (a)  θ-2θ x-ray diffraction patterns for various thin film heterostructures reveal single-phase, epitaxial films on all substrates. (b) Specular ω-rocking curves about the 200 diffraction peak of PbZr0.2Ti0.8O3 reveal an increasing fraction of a domains with increasing tensile strain from SrTiO3 to GdScO3.